Question: What's the first wrong statement in the proof below that $ \triangle CEB \cong \triangle DEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle DBE \cong \angle CFE$ $, \ $ $ \overline{BE} \cong \overline{EF}$ $, \ $ $ \angle BED \cong \angle CEF$ $, \ $ $ \overline{BE} \cong \overline{AB}$ $, \ $ $ \angle BED \cong \angle BAC$ $, \ $ and $\ $ $ \angle BDE \cong \angle ACB$ Proof $ \triangle CEF \cong \triangle DEB$ because ASA $ \angle BDE \cong \angle ECF$ because vertical angles are equal $ \overline{CE} \cong \overline{DE}$ because corresponding parts of congruent triangles are congruent $ \overline{BD} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \triangle CAB \cong \triangle DEB$ because AAS $ \triangle CEB \cong \triangle DEB$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle ECF \cong \angle BDE$ is the first wrong statement.